The problem statement, all variables and given/known data Let f, f1, f2, f3, ... be continuous real-valued functions on the compact metric space E, with f = lim fn. Prove that if fi ≤ fj whenever i ≤ j, then f1, f2, ... converges uniformly. The attempt at a solution I was trying to reverse engineer the proof, but I'm stuck trying to figure out how the hypothesis, viz. fi ≤ fj whenever i ≤ j, comes into play. Any tips?